Theoretical analysis of the exponential transversal method of lines for the diffusion equation

A new approximate technique to solve the diffusion equation, called the Exp onential Transversal Method of Lines (ETMOL), utilizes an exponential varia tion of the dependent variable to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide range of heat/mass transfer applications and have obtained surprisingly goo d numerical results. In this article, we study the theoretical properties o f ETMOL in depth. In particular, consistency, stability, and convergence ar e established within the framework of the heat/mass diffusion equation. In most practical applications, the new method presents a very reduced truncat ion error in time, and its different versions are proven to be unconditiona lly stable in the Fourier sense. Convergence of the approximate solutions h ave then been established. The theory is corroborated by several analytical /numerical experiments that pose different levels of complexity. (C) 2000 J ohn Wiley & Sons, Inc.